This paper is concerned with a generalized 2D parabolic equation with a nonautonomous perturbation −∆ut + α ∆ut + μ∆ u+∇ · −→ F (u) +B(u, u) = ǫg(x, t). Under some proper assumptions on the external force term g, the upper semicontinuity of pullback attractors is proved. More precisely, it is shown that the pullback attractor {Aǫ(t)}t∈R of the equation with ǫ > 0 converges to the global attract...

The aim of this paper is to prove the existence of a global attractor for a semilinear degenerate parabolic equation involving the Grushin operator.

Fractal Interpolation Function is the attractor of Iterated Function System (IFS), to overcome the weakness of IFS that IFS only reflect the similarity between global region and local region of a graph, Barnsley put forward the Recurrent Iterated Function System and the Recurrent Fractal Interpolation Function. RIFS reflect the similarity between local and local, it can make more complicated gr...

Strength of attractor is studied by the return rate to itself after perturbations, for a multi-attractor state of a globally coupled map. It is found that fragile (Milnor) attractors have a large basin volume at the partially ordered phase. Such dominance of fragile attractors is understood by robustness of global attraction in the phase space. Change of the attractor strength and basin volume ...

A class of skew products over irrational rotations of the circle is defined which contains some systems which have strange nonchaotic attractors. The global attractor of these systems is characterized: it lies between an upper semi-continuous curve and a lower semi-continuous curve. With additional assumptions on the class of maps considered more detail of the attractor can be given. Mathematic...

This paper investigates the global synchronization method of two identical systems and two different chaotic systems. The proposed method is effective and convenient to synchronize two identical systems and two different chaotic systems by using nonlinear control functions. The method has been applied successfully to make two identical four-scroll attractor and also two different chaotic system...

In this paper it is shown how to model times series by using random iterated neural networks with place-dependent probabilities. The model assumes that the time series comes from a dynamical system which has a compact global attractor and a physical probability measure supported on the attractor. Also, an evolutionary algorithm is used to train a random iterated neural network that models a nan...